the integer n 3510593 has hexadecimal

Question

The integer n = 3,510,593 has hexadecimal representation 0x00359141 (check this with your d2h program), while the double precision, floating-point number 3510593.0 has hexadecimal representation 0x414ac8a080000000.  Derive this floating-point representation and explain the correlation between the bits of the integer and floating-point representations.

Here is a recommended procedure:

1.      Write the binary representation of n.  (Do you want to start from decimal 3510593 or hexadecimal 359141?)

2.      Insert a decimal (binary) point, and write n as 1.xxx ... x ´ 2^E

3.      Write (E + BIAS) in binary.  (What is BIAS for a double?)

4.      Assemble the floating point representation of  (double)n  from the data you have collected.  How long is the longest run of matching bits in your answers to steps 1 and 4?

             Longest match is _______ bits.

More information about floating-point formats can be found in Section 2.4.2 of the text and the handout binfloat.pdf in the Piazza "General Resources" section.